Kardashian, 29, has been trying to remain upbeat as reports surfaced of her husband Lamar Odom's alleged infidelities and battle with drug issues.

"She's very sensitive and she loves really hard and she feels with all of her soul, but she also has the ability to put that game face on and go out there in the world and do what she needs to do," Jenner says.

Kardashian – who has been living separately from her NBA star husband – has been posting inspirational messages on Twitter, but a source tells PEOPLE that "she doesn't know" if her marriage can be saved.

"It doesn't seem like a reconciliation is any closer to happening," the source says.